Question

Evaluate
-2
/√5x-4- √5x-2
dx​

Answer 1

  Answer:

$\frac{2}{15} [ (5x-4)^{3/2} + (5x-2)^{3/2} ] + C$

Step-by-step explanation:

$\int\limits {\frac{-2}{\sqrt{5x-4}-\sqrt{5x-2} } \, dx$

Multiplying numerator and denominator by $\sqrt{5x-4} + \sqrt{5x-2}$

= $-2\int\limits {\frac{\sqrt{5x-4} +\sqrt{5x-2} }{5x-4-(5x-2)} } \, dx$

=$-2\int\limits {\frac{\sqrt{5x-4} + \sqrt{5x-2} }{-2} } \, dx$

=$\int\limits {\sqrt{5x-4} +\sqrt{5x-2} } \, dx$

=$\int\limits {(\sqrt{5x-4} )} \, dx +\int\limits {\sqrt{5x-2} } \, dx$

=$\ {\frac{(5x-4)^{3/2} }{3/2*5} } + \frac{(5x-2)^{3/2} }{3/2*5} +C$

= $2/15[(5x-4)^{3/2} +(5x-2^{3/2}] + C$